The cosmic microwave background power spectra are a primary window into the early universe. However, achieving interpretable compression and fast inference diagnostics under weak model assumptions remains challenging. We propose a parameter-conditioned variational autoencoder (CVAE) that aligns a data-driven latent representation with cosmological parameters while retaining an interface to likelihood-style diagnostic tests. The model achieves high directional reconstruction fidelity for the $D_{\ell }^{TT}$, $D_{\ell }^{EE}$, and $D_{\ell }^{TE}$ spectra in just five latent dimensions. It reconstructs spectra for several test cases beyond the $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model, including controlled parameter extrapolations, and enables an amortized surrogate diagnostic that reduces one representative post-training Markov chain Monte Carlo run from $\sim 40$ hours on CPU cores to $\sim 2\mathrm{minutes}$ on a graphics processing unit in this demonstration. The learned latent space shows a distributed, partially structured organization that mirrors known cosmological parameters and their degeneracies. It also provides representation-space discrimination diagnostics for distinguishing tested cosmological spectra from a fiducial reference. Overall, this physics-informed CVAE supports interpretable compression, rapid diagnostic exploration, and anomaly-sensitive representation learning beyond $\mathrm{\Lambda }\mathrm{CDM}$.

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• Cosmic microwave background
• Cosmological parameters
• Cosmology
• Dark energy
• Deep learning
• Unsupervised learning